(a^2b^3)^2/(ab)^-2

Jasonbradley

2 min read

·

Jun 16, 2024

18

Share

Simplifying Algebraic Expressions: (a^2b^3)^2/(ab)^-2

This article will guide you through the process of simplifying the algebraic expression (a^2b^3)^2/(ab)^-2. We will break down the steps and explain the rules involved.

Understanding the Rules

Before we start simplifying, let's recall some key rules of exponents:

• Power of a power: (x^m)^n = x^(m*n)
• Negative exponent: x^-n = 1/x^n
• Division of powers: x^m / x^n = x^(m-n)

Simplifying the Expression

1. Apply the power of a power rule to both numerator and denominator:

   • (a^2b^3)^2 = a^(22) * b^(32) = a^4b^6
   • (ab)^-2 = a^(-21) * b^(-21) = a^-2b^-2

2. Apply the negative exponent rule to the denominator:

   • a^-2b^-2 = 1/(a^2b^2)

3. Rewrite the expression with the simplified terms:

   • (a^2b^3)^2 / (ab)^-2 = (a^4b^6) / (1/(a^2b^2))

4. Dividing by a fraction is the same as multiplying by its reciprocal:

   • (a^4b^6) / (1/(a^2b^2)) = (a^4b^6) * (a^2b^2/1)

5. Multiply the terms in the numerator:

   • (a^4b^6) * (a^2b^2) = a^(4+2) * b^(6+2) = a^6b^8

Final Simplified Expression

Therefore, the simplified form of the expression (a^2b^3)^2/(ab)^-2 is a^6b^8.